A diesel particulate filter (hereinafter referred to as DPF) which traps particulate matter contained in the exhaust gas of a diesel engine for a vehicle performs regeneration by burning the trapped particulate matter when the amount of trapped particulate matter reaches a certain level, and thus becomes able to trap particulate matter again. The amount of trapped particulate matter is determined by estimate from the operating condition of the vehicle. DPF regeneration is performed by raising the exhaust gas temperature of the engine to burn the particulate matter.